Theoretical analysis for a class of rheonomous affine constraints on configuration manifolds. I: Fundamental properties and integrability/nonintegrability conditions (Q1954904)

Summary: We analyze a class of rheonomous affine constraints defined on configuration manifolds from the viewpoint of integrability/nonintegrability. First, we give the definition of \(A\)-rheonomous affine constraints and introduce, geometric representation their. Some fundamental properties of the \(A\)-rheonomous affine constrains are also derived. We next define the rheonomous bracket and derive some necessary and sufficient conditions on the respective three cases: complete integrability, partial integrability, and complete nonintegrability for the \(A\)-rheonomous affine constrains. Then, we apply the integrability/nonintegrability conditions to some physical examples in order to confirm the effectiveness of our new results.